Asymptotics for the maximum likelihood estimators of diffusion models

dc.contributorPark, Joon Y.
dc.creatorJeong, Minsoo
dc.date.accessioned2010-01-15T00:03:15Z
dc.date.accessioned2010-01-16T00:27:38Z
dc.date.accessioned2017-04-07T19:55:04Z
dc.date.available2010-01-15T00:03:15Z
dc.date.available2010-01-16T00:27:38Z
dc.date.available2017-04-07T19:55:04Z
dc.date.created2008-12
dc.date.issued2009-05-15
dc.description.abstractIn this paper I derive the asymptotics of the exact, Euler, and Milstein ML estimators for diffusion models, including general nonstationary diffusions. Though there have been many estimators for the diffusion model, their asymptotic properties were generally unknown. This is especially true for the nonstationary processes, even though they are usually far from the standard ones. Using a new asymptotics with respect to both the time span T and the sampling interval ?, I find the asymptotics of the estimators and also derive the conditions for the consistency. With this new asymptotic result, I could show that this result can explain the properties of the estimators more correctly than the existing asymptotics with respect only to the sample size n. I also show that there are many possibilities to get a better estimator utilizing this asymptotic result with a couple of examples, and in the second part of the paper, I derive the higher order asymptotics which can be used in the bootstrap analysis.
dc.identifier.urihttp://hdl.handle.net/1969.1/ETD-TAMU-2335
dc.language.isoen_US
dc.subjectnonstationary diffusion process
dc.subjectmixed normal limit theory
dc.subjectMilstein scheme
dc.subjectEuler scheme
dc.subjectmaximum likelihood estimation
dc.subjecttrue transition density
dc.subjecthypothesis testing
dc.titleAsymptotics for the maximum likelihood estimators of diffusion models
dc.typeBook
dc.typeThesis

Files